Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (4): 492-502.

Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

School of Mathematical Sciences, Anhui University

Received:2011-11-15 Online:2013-12-30 Published:2023-02-16
About author:ZHOU Ling(1988-),female,native of Funan,Anhui,a postgraduate of Anhui University, engages in functional diﬀerential equation; ZHOU Zong-fu(1964-), male, native of Hefei, Anhui, a professor of Anhui University, engages in functional diﬀerential equation(corresponding author).
Supported by:
Supported by the National Natural Science Foundation of China(11071001)； Supported by the 211 Project of Anhui University(KJTD002B)； Supported by the Natural Science Foundation of Anhui Province(1208085MAB)

Abstract

Abstract: By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows (φp((x(t).. cx(t.. σ)) ′′)) ′ +f1(x(t))x ′(t) + f2(x ′(t))x ′′(t) +g(t, x(t), x(t.. τ(t)), ∫ 0-rx(t + s) dm(s))=e(t). Some new results for existence of T-periodic solutions to such equations are obtained.

Key words: periodic solutions, deviating argument, coincidence degree, p-Laplacian equations

CLC Number:

O178.1

ZHOU Ling, ZHOU Zong-fu, SHEN Qin-rui. Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(4): 492-502.

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Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

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